Editing Quantum Error Correction (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'The Error Overhead' (Calculating the cost of a logical qubit):'''
<syntaxhighlight lang="python">
def calculate_overhead(physical_error_rate, target_logical_qubits):
    """
    As physical errors go down, we need fewer qubits to fix them.
    (Simplified model)
    """
    if physical_error_rate < 0.001:
        qubits_per_logical = 100
    elif physical_error_rate < 0.01:
        qubits_per_logical = 1000
    else:
        return "IMPOSSIBLE: Error rate is above the threshold."
        
    total_physical = target_logical_qubits * qubits_per_logical
    return {
        "Logical Qubits Needed": target_logical_qubits,
        "Physical Qubits Required": f"{total_physical:,}",
        "Overhead Factor": qubits_per_logical
    }

# To run Shor's Algorithm, we need ~2,000 Logical Qubits.
# If our hardware is 'okay' (1% error):
print(calculate_overhead(0.01, 2000))
# We need 2 MILLION physical qubits to get 2,000 good ones!
</syntaxhighlight>

; QEC Landmarks
: '''Shor's 9-Qubit Code (1995)''' → Peter Shor proved that it was possible to fix both "Bit-flips" and "Phase-flips" using a group of 9 entangled qubits.
: '''The Surface Code (2012)''' → The breakthrough design that allows qubits to be laid out like a "Chessboard," which is much easier to build than complex 3D networks.
: '''Google Sycamore QEC (2023)''' → Google proved for the first time that "Scaling up" the number of qubits actually made the error rate go **Down**, proving the theory works in the real world.
: '''Logical Qubits at Harvard (2023)''' → Scientists successfully created 48 logical qubits and ran error-corrected algorithms for the first time.
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